search for the qcd critical point
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Gary Westfall for STAR – Erice, 2012 1
Search for the QCD Critical Point
Gary D. WestfallMichigan State University
For the STAR Collaboration
Gary Westfall for STAR – Erice, 2012 2
Search for Possible QCD Critical PointTrajectories at low μB
Theories suggest a cross-over transition
Trajectories at high μB
Theories suggest a first-order transition
Finding the CP theoretically is difficult
Search for the CP experimentally
arXiv:1007.2613
Gary Westfall for STAR – Erice, 2012 3
The RHIC Beam Energy Scan
√sNN (GeV) Min. Bias Events (106)
7.7 4.311.5 11.719.6 35.827 70.439 130.4
62.4 67.3200 500
• Goals:• Search for signatures of a possible
phase transition from hadronic matter to quark gluon matter
• Search for signatures of a possible QCD critical point
•Strategy• Vary incident energy to span range inT-μB
• Look for non-monotonic behavior of observables
Gary Westfall for STAR – Erice, 2012 4
Observables• Particle ratio fluctuations
• K/π• Strangeness fluctuations
• p/π• Baryon fluctuations
• K/p• Strangeness/baryon correlations
• Net particle higher moments• Net charge
• Net charge fluctuations• Net kaons
• Net strangeness fluctuations• Net protons
• Net baryon fluctuations
Gary Westfall for STAR – Erice, 2012 5
Observable - Fluctuations • Our observable is νdyn,Kπ, which measures how
correlated the event-by-event distributions are
• νdyn,Kπ, is zero for uncorrelated emission (Poisson)
• NA49 uses σdyn
• With enough statistics and large denominator
dyn, 2 2
1 12K K K
KKK
N N N N N NN NN N
2 2 2 2dyn data mixed data mixedsgn( ) | |
Gary Westfall for STAR – Erice, 2012 6
Observable – Net Particle Moments • Fluctuations of conserved quantities such as net charge,
net strangeness, and net baryon number may be related to the chiral phase transition or critical phenomena• Net charge
• Net strangeness
• Net baryon number
• Higher moments of the net particle distributions are predicted to be sensitive to high powers of the susceptibility
Gary Westfall for STAR – Erice, 2012 7
Cumulants• To describe the higher moments of net particle
distributions, we employ cumulants• Cumulants can be expressed in terms of the
central moments• The central moments are defined by
Gary Westfall for STAR – Erice, 2012 8
Cumulants• The first four cumulants are
• We can then define
• Near the critical point, the cumulants will diverge with large powers of the correlation length (ξ)
• Higher moments scale with higher powers of the correlation length
Gary Westfall for STAR – Erice, 2012 9
Cumulants• The susceptibilities χ and correlation lengths ξ scale as
• Various theories predict large enhancements in C4/C2 for net charge, net strangeness, and net baryon number• Karsch et al., PLB 695, 136 (2011). arXiv: 1203.0784• Cheng et al., PRD 79, 074505 (2009)• Hatta et al., PRL 91, 102003 (2003), Hatta et al. PRD 67, 014028
(2003)• Gavai, Gupta. PLB, 696, 459 (2011)• Stephanov PRL 102, 032301 (2009)
Gary Westfall for STAR – Erice, 2012 10
Expectations for Net Particle Moments
• We can define two expectations for net particle moments• Poisson distribution
• We assume that the positive particle multiplicity and the negative particle multiplicity distributions are described by Poisson distributions characterized by μ+ and μ-
• Negative binomial/binomial distribution• We assume that the positive particle multiplicity and the
negative particle multiplicity distributions are described by negative binomial/binomial distributions characterized by (μ+,σ2+) and (μ-,σ2-)
Gary Westfall for STAR 11
Difference of Two Negative Binomials/Binomials• The positive particle and negative particle
multiplicity distributions are negative binomials or binomial distributions, depending on μ/σ2
• The positive and negative multiplicity distributions can be characterized by their cimmulants:
• The cumulants of the differences of the two cumulants are
• The products of the moments are then
Ole E. Barndorff-Nielsen, David G. Pollard and Neil ShephardDISCRETE-VALUED LEVY PROCESSES AND LOWLATENCY FINANCIAL ECONOMETRICSOxford, ISSN 1471-0498
Gary Westfall for STAR 12
Difference of Two Poisson Distributions• μ+ = mean of the positive particle distribution• μ- = mean of the negative particle distribution• The cumulants of a Poisson distribution are given
by
• So the cumulants of the difference are
• The moment ratios are
Same result as Skellam distribution
Gary Westfall for STAR – Erice, 2012 13
K/π Fluctuations – Summed Signs• (K++K-)/(π++π -)
• Central events(0 - 5%)
• STAR data show no significant energy dependence
• There appears to be a disagreement between STAR and NA49 results below 19.6 GeV
• The UrQMD model shows little energy dependence and over-predicts the fluctuations
STAR: Prithwish Tribedy, QM 2012NA49: C. Alt et al. Phys. Rev. C 79, 044910 (2009)
Gary Westfall for STAR – Erice, 2012 14
K/π Fluctuations – Separated Signs
• K+/π - is strongly negative due to decays, possible candidate is
• K+/π+ is also negative, needs further study to investigate the origin
*(892)K K STAR: Prithwish Tribedy, QM 2012
Gary Westfall for STAR – Erice, 2012 15
p/π Fluctuations – Summed Signs
dyn, 2 2
1 12
p p pp
pp
N N N NN N
N NNN
• (p+ )/(π++π -)• Central events(0 – 5%)
• STAR results show a smooth decrease with decreasing incident energy
• There is good agreement between STAR and NA49 results
• The UrQMD model agrees with the data at low energy, but changes sign at high energy
STAR: Prithwish Tribedy, QM 2012NA49: C. Alt et al. Phys. Rev. C 79, 044910 (2009)
Gary Westfall for STAR – Erice, 2012 16
p/π Fluctuations – Same Signs
• p+/π+
• p-/π -
• Central events(0 – 5%)
• Little energy dependence for positive signs
• Very few antiprotons at the lowest energy
STAR: Prithwish Tribedy, QM 2012
Gary Westfall for STAR – Erice, 2012 17
p/π Fluctuations – Opposite Signs
• p+/π -
• p-/π+
• Central events(0 – 5%)
• Little energy dependence forp+/π -
• Very few antiprotons at the lowest energy
STAR: Prithwish Tribedy, QM 2012
Gary Westfall for STAR – Erice, 2012 18
K/p Fluctuations – Summed Signs• (p+ )/(K++K-)
• Central events (0 - 5%)
• STAR results decrease smoothly with decreasing incident energy
• The seems to be disagreement between STAR and NA49 results at 7.7 GeV
• The UrQMD model over-predicts the fluctuations and changes sign at high energy
STAR: Prithwish Tribedy, QM 2012NA49: T. Anticic et al., PRC 83, 061902(R) (2011)
Gary Westfall for STAR – Erice, 2012 19
K/p Fluctuations – Same Sign
• K+/p+
• K-/p -
• Central events(0 – 5%)
• Little energy dependence
STAR: Prithwish Tribedy, QM 2012
Gary Westfall for STAR – Erice, 2012 20
K/p Fluctuations – Opposite Sign
• K+/p–
• K-/p+
• Central events(0 – 5%)
• Little energy dependence
• Very few antiprotons at the lowest energy
STAR: Prithwish Tribedy, QM 2012
Gary Westfall for STAR – Erice, 2012 21
K+/p+ Fluctuations – Compare NA49
• K+/p+
• Central events
• Disagreement between STAR and NA49 at lowest energies
STAR: Prithwish Tribedy, QM 2012NA49: T. Anticic et al., PRC 83, 061902(R) (2011)
Gary Westfall for STAR – Erice, 2012 22
Net Charge MomentsEnergy Dependence
STAR: Daniel McDonald, QM 2012Au+Au 0-5%
Karsch, Redlich, PLB 695, 136 (2011)
Gary Westfall for STAR – Erice, 2012 23
Net Kaon MomentsEnergy Dependence
STAR: Daniel McDonald, QM 2012Au+Au 0-5%
Gary Westfall for STAR – Erice, 2012 24
Net Proton MomentsEnergy Dependence
STAR: Xiaofeng Luo, QM 2012
Gary Westfall for STAR – Erice, 2012 25
Conclusions – Particle Ratio Fluctuations• Particle ratio fluctuations in central collisions
• K/π• Summed sign fluctuations are positive• Separate sign fluctuations are negative• Disagreement with NA49 at lowest energy
• p/π• Summed sign fluctuations are negative• Separate sign fluctuations are negative• Agreement with NA49
• K/p• Summed sign fluctuations are negative• Separate sign fluctuations are negative• Disagreement with NA49 at lowest energy
• No non-monotonic behavior observed with incident energy
Gary Westfall for STAR – Erice, 2012 26
Conclusions – Net Particle Higher Moments• Net particle higher moments in central collisions
• Net charge• Sσ = C3/C2 consistent with negative binomial/binomial expectation, above
Poisson expectation, and below HRG• κσ2 = C4/C2 between Poisson and negative binomial/binomial expectations
and consistent with HRG• Net kaons
• Sσ = C3/C2 consistent with both the Poisson and negative binomial/binomial expectations
• κσ2 = C4/C2 consistent with both Poisson and negative binomial/binomial expectations
• Net protons• Sσ = C3/C2 consistent with both the Poisson and negative binomial/binomial
expectations• κσ2 = C4/C2 below Poisson expectation but more consistent with the
negative binomial/binomial expectation• No non-monotonic behavior observed with incident energy
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